This Common Core-aligned 6th Grade Math course builds on the foundations established in the 5th Grade course and expands students’ understanding of number, operations, algebraic thinking, geometry, and data analysis. Students deepen their fluency with ratios, rates, percentages, multi-digit division, fraction division, decimals, rational numbers, expressions, equations, geometry, and statistics.
Throughout the course, students learn to represent quantitative relationships in tables, graphs, diagrams, and equations; solve real-world problems involving proportional reasoning, unit rates, percentages, and measurement conversions; and reason flexibly about numerical and algebraic structure. They also develop a stronger understanding of negative numbers, the coordinate plane, exponents, geometric measurement, and statistical summaries and displays.
Students begin by studying ratios, equivalent ratios, ratio tables, tape diagrams, unit rates, percentages, and unit conversions. They then extend their fluency with whole number division, fraction division, and decimal operations, while strengthening their understanding of place value and the meaning of division in increasingly complex settings.
The course next introduces rational numbers, including negative numbers, absolute value, ordering rational numbers, coordinate plane reasoning, and exponents. Students then transition into expressions and equations, where they learn to write, evaluate, simplify, and factor algebraic expressions; solve one-step equations; represent inequalities; and analyze two-variable relationships using tables and graphs.
In geometry, students investigate area, perimeter, surface area, volume, symmetry, and coordinate geometry. The course concludes with statistics and probability, where students summarize distributions using measures of center and spread, interpret outliers, and represent data using frequency tables, dot plots, box plots, and histograms.
| 1.1.1. | Introduction to Ratios | |
| 1.1.2. | Equivalent Ratios | |
| 1.1.3. | Writing Ratios Using Fractions | |
| 1.1.4. | Comparing Ratios | |
| 1.1.5. | Approximating Ratios | |
| 1.1.6. | Reasoning With Equivalent Ratios | |
| 1.1.7. | Further Reasoning With Equivalent Ratios |
| 1.2.1. | Ratio Tables | |
| 1.2.2. | Graphing Ratios | |
| 1.2.3. | Tape Diagrams |
| 1.3.1. | Unit Rates | |
| 1.3.2. | Solving Problems Using Unit Rates | |
| 1.3.3. | Speed as a Unit Rate |
| 1.4.1. | Understanding Percentages Using Models | |
| 1.4.2. | Converting Between Percentages and Fractions | |
| 1.4.3. | Converting Between Percentages and Decimals | |
| 1.4.4. | Comparing Fractions, Percents, and Decimals |
| 1.5.1. | Finding a Percentage Given Two Numbers | |
| 1.5.2. | Finding Part of a Number Given a Whole and a Percentage | |
| 1.5.3. | Finding a Total Given a Part and a Percentage | |
| 1.5.4. | Finding a Percentage Given Two Numbers: Word Problems | |
| 1.5.5. | Finding Part of a Number Given a Whole and a Percentage: Word Problems |
| 1.6.1. | Converting Metric Units of Length to Larger Units | |
| 1.6.2. | Converting Customary Units of Length to Larger Units | |
| 1.6.3. | Converting Units to of Length to Larger Units Using Long Division | |
| 1.6.4. | Converting Units of Volume to Larger Units | |
| 1.6.5. | Converting Units of Mass to Larger Units | |
| 1.6.6. | Converting Units of Time to Larger Units |
| 2.7.1. | Two-Digit by One-Digit Division | |
| 2.7.2. | Three-Digit by One-Digit Division | |
| 2.7.3. | Four-Digit by One-Digit Division | |
| 2.7.4. | Using Fractions to Represent Division of Whole Numbers | |
| 2.7.5. | Dividing Numbers by One-Digit Numbers With Rounding | |
| 2.7.6. | Dividing Numbers by One-Digit Numbers: Interpreting the Remainder |
| 2.8.1. | Three-Digit by Two-Digit Division | |
| 2.8.2. | Four-Digit by Two-Digit Division | |
| 2.8.3. | Dividing by Two-Digit Numbers by Connecting Multiplication and Division | |
| 2.8.4. | Dividing by Two-Digit Numbers With Remainders by Connecting Multiplication and Division | |
| 2.8.5. | Estimating Multi-Digit Division |
| 3.9.1. | Dividing Whole Numbers by Fractions Using Models: Whole Number Results | |
| 3.9.2. | Dividing Whole Numbers by Fractions Using Models: Fractional Results | |
| 3.9.3. | Dividing Fractions by Whole Numbers Using Models | |
| 3.9.4. | Dividing Whole Numbers by Fractions | |
| 3.9.5. | Dividing Fractions by Whole Numbers | |
| 3.9.6. | Dividing Fractions and Whole Numbers: Word Problems |
| 3.10.1. | Reciprocals | |
| 3.10.2. | Dividing Fractions Using Models | |
| 3.10.3. | Dividing Fractions | |
| 3.10.4. | Dividing Fractions: Word Problems | |
| 3.10.5. | Finding Side Lengths Using Fraction Division |
| 3.11.1. | Dividing Mixed Numbers by Whole Numbers | |
| 3.11.2. | Dividing Whole Numbers by Mixed Numbers | |
| 3.11.3. | Dividing Fractions by Mixed Numbers | |
| 3.11.4. | Dividing Mixed Numbers by Fractions | |
| 3.11.5. | Dividing Mixed Numbers | |
| 3.11.6. | Dividing Mixed Numbers: Word Problems |
| 4.12.1. | Adding Decimals | |
| 4.12.2. | Subtracting Decimals | |
| 4.12.3. | Addition With Unequal Numbers of Decimals | |
| 4.12.4. | Subtraction With Unequal Numbers of Decimals |
| 4.13.1. | Multiplying a Decimal by a Multi-Digit Whole Number | |
| 4.13.2. | Multiplying Two-Digit Decimals | |
| 4.13.3. | Multiplying Two-Digit Decimals by Three-Digit Decimals | |
| 4.13.4. | Multiplying Three-Digit Decimals |
| 4.14.1. | Division of Whole Numbers With Decimal Quotients | |
| 4.14.2. | Division of Whole Numbers With Decimal Quotients and Rounding | |
| 4.14.3. | Dividing Decimals Using Place Value Strategies | |
| 4.14.4. | Dividing Decimals Using the Standard Algorithm | |
| 4.14.5. | Dividing Three-Digit Decimals by Two-Digit Decimals | |
| 4.14.6. | Dividing Four-Digit and Five-Digit Decimals | |
| 4.14.7. | Estimating Decimal Division | |
| 4.14.8. | Estimating Multi-Digit Division With Decimals |
| 5.15.1. | Negative Numbers | |
| 5.15.2. | Absolute Value | |
| 5.15.3. | Comparing Negative Numbers | |
| 5.15.4. | Interpreting Negative Numbers | |
| 5.15.5. | Interpreting Absolute Value |
| 5.16.1. | Natural Numbers, Integers, and Rational Numbers | |
| 5.16.2. | Identifying Rational Numbers on a Number Line | |
| 5.16.3. | Comparing Rational Numbers | |
| 5.16.4. | Ordering Rational Numbers |
| 5.17.1. | The Cartesian Coordinate System | |
| 5.17.2. | Rational Numbers in the Coordinate Plane | |
| 5.17.3. | Reflections of Points in the Coordinate Plane | |
| 5.17.4. | Solving Problems in the Coordinate Plane |
| 5.18.1. | Introduction to Exponents | |
| 5.18.2. | Evaluating Exponents | |
| 5.18.3. | Evaluating Larger Exponents | |
| 5.18.4. | Evaluating Exponents With Fractional Bases | |
| 5.18.5. | Evaluating Exponents With Decimal Bases | |
| 5.18.6. | Comparing Exponents | |
| 5.18.7. | Evaluating Whole Number Expressions Containing Exponents |
| 6.19.1. | Introduction to Algebraic Expressions | |
| 6.19.2. | Constructing Algebraic Expressions | |
| 6.19.3. | Evaluating Linear Expressions | |
| 6.19.4. | Evaluating Algebraic Expressions | |
| 6.19.5. | Identifying Terms in Linear Expressions | |
| 6.19.6. | Identifying Coefficients and Constants | |
| 6.19.7. | Identifying Like Terms in Linear Expressions | |
| 6.19.8. | The Greatest Common Factor of Two Linear Expressions |
| 6.20.1. | Simplifying Linear Expressions | |
| 6.20.2. | Applying the Distributive Law to Linear Expressions | |
| 6.20.3. | Factoring Linear Expressions | |
| 6.20.4. | Identifying Equivalent Expressions |
| 6.21.1. | Identifying Solutions to Linear Equations | |
| 6.21.2. | One-Step Addition Equations | |
| 6.21.3. | One-Step Subtraction Equations | |
| 6.21.4. | One-Step Multiplication Equations | |
| 6.21.5. | One-Step Multiplication Equations Containing Fractions | |
| 6.21.6. | One-Step Division Equations | |
| 6.21.7. | Modeling Real-World Problems Using One-Step Equations | |
| 6.21.8. | Solving Real-World Problems Using One-Step Equations |
| 6.22.1. | Identifying Solutions to Linear Inequalities | |
| 6.22.2. | Representing Inequalities on Number Lines | |
| 6.22.3. | Modeling Real-World Problems Using Inequalities |
| 6.23.1. | Introduction to Two-Variable Equations | |
| 6.23.2. | Two-Variable Equations: Solving for the Independent Variable | |
| 6.23.3. | Analyzing Two-Variable Equations Using Tables | |
| 6.23.4. | Analyzing Two-Variable Equations Using Graphs |
| 7.24.1. | Units of Area and Volume | |
| 7.24.2. | Areas of Rectangles | |
| 7.24.3. | Areas of Right Triangles | |
| 7.24.4. | Areas of Triangles | |
| 7.24.5. | Areas and Perimeters of Parallelograms | |
| 7.24.6. | Finding Areas of Polygons Using Decomposition | |
| 7.24.7. | Finding Areas Between Shapes | |
| 7.24.8. | Lines of Symmetry |
| 7.25.1. | Identifying Three-Dimensional Shapes | |
| 7.25.2. | Faces, Vertices, and Edges of Polyhedrons | |
| 7.25.3. | Nets of Polyhedrons | |
| 7.25.4. | Finding Surface Areas Using Nets | |
| 7.25.5. | Volumes of Right Rectangular Prisms | |
| 7.25.6. | Volumes of Right Rectangular Prisms: Word Problems | |
| 7.25.7. | Volumes of Rectangular Prisms With Fractional Edge Lengths | |
| 7.25.8. | Volumes of Rectangular Prisms With Fractional Edge Lengths: Word Problems |
| 7.26.1. | Distances Between Points in the Coordinate Plane | |
| 7.26.2. | Polygons in the Coordinate Plane | |
| 7.26.3. | Finding Areas and Perimeters in the Coordinate Plane |
| 8.27.1. | Introduction to Statistics | |
| 8.27.2. | The Mean of a Data Set | |
| 8.27.3. | The Median of a Data Set | |
| 8.27.4. | The Mode of a Data Set | |
| 8.27.5. | Range, Quartiles, and IQR | |
| 8.27.6. | Mean Absolute Deviation | |
| 8.27.7. | Outliers | |
| 8.27.8. | Removing Outliers | |
| 8.27.9. | Comparing Measures of Center | |
| 8.27.10. | Comparing Measures of Spread |
| 8.28.1. | Frequency Tables | |
| 8.28.2. | Dot Plots | |
| 8.28.3. | Box Plots | |
| 8.28.4. | Histograms | |
| 8.28.5. | Measuring Centrality From Dot Plots | |
| 8.28.6. | Measuring Range and MAD From Dot Plots | |
| 8.28.7. | Measuring Quartiles and IQR From Dot Plots | |
| 8.28.8. | Symmetry, Skew, and Outliers |
